THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary,

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1 High School Level Glossary Geometry Glossary / Chinese Simplified Translation of Geometry terms based on the Coursework for Geometry Grades 9 to 12. Word-for-word glossaries are used for testing accommodations for ELL/LEP students THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Last Updated: June 2016

2 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary, and Continuing Education and Office of Higher Education Office of Bilingual Education and Foreign Language Studies THE UNIVERSITY OF THE STATE OF NEW YORK Regents of the University MERRYL H. TISCH, Chancellor, B.A., M.A., Ed.D.... New York MILTON L. COFIELD, Vice Chancellor, B.S., M.B.A., Ph.D.... Rochester ROBERT M. BENNETT, Chancellor Emeritus, B.A., M.S.... Tonawanda SAUL B. COHEN, B.A., M.A., Ph.D... New Rochelle JAMES C. DAWSON, A.A., B.A., M.S., Ph.D.... Plattsburgh ANTHONY S. BOTTAR, B.A., J.D.... Syracuse GERALDINE D. CHAPEY, B.A., M.A., Ed.D.... Belle Harbor HARRY PHILLIPS, 3rd, B.A., M.S.F.S.... Hartsdale JOSEPH E. BOWMAN, JR., B.A., M.L.S., M.A., M.Ed., Ed.D... Albany JAMES R. TALLON, JR., B.A., M.A.... Binghamton ROGER TILLES, B.A., J.D.... Great Neck KAREN BROOKS HOPKINS, B.A., M.F.A... Brooklyn CHARLES R. BENDIT, B.A.... Manhattan BETTY A. ROSA, B.A., M.S. in Ed., M.S. in Ed., M.Ed., Ed.D... Bronx LESTER W. YOUNG, JR., B.S., M.S., Ed. D.... Oakland Gardens CHRISTINE D. CEA, B.A., M.A., Ph.D.... Staten Island WADE S. NORWOOD, B.A.... Rochester Interim President of the University and Commissioner of Education CAROLE F. HUXLEY Senior Deputy Commissioner of Education, P 16 JOHANNA DUNCAN-POITIER Associate Commissioner for Curriculum and Instructional Support JEAN STEVENS Coordinator, Office of Bilingual Education and Foreign language Studies PEDRO J. RUIZ Acknowledgements: The New York State Education Department Glossaries for Language Learners were reviewed and updated during the school year. We would like to thank in these efforts the New York State Education Department Language BETACs (Spanish, Asian and Haitian Bilingual Education Technical Assistance Centers), the NYS Office of Curriculum, Instruction and Instructional Technology; the New York City Department of Education Office of Language Learners, and the NYC Department of Education Translation and Interpretation Unit. The State Education Department does not discriminate on the basis of age, color, religion, creed, disability, marital status, veteran status, national origin, race, gender, genetic predisposition or carrier status, or sexual orientation in its educational programs, services and activities. Portions of this publication can be made available in a variety of formats, including brailed, large print or audio tape, upon request. Inquiries concerning this policy of nondiscrimination should be directed to the Department s Office for Diversity, Ethics, and Access, Room 530, Education Building, Albany, NY

3 Problem Solving AA triangle similarity AAA triangle similarity AAS triangle congruence additive property of equality algorithm apply ASA triangle congruence conjecture constraints construct discover dynamic geometry software explore generalization inductive reasoning justify parameters reason truth value valid argument Reasoning and Proof AA triangle similarity AAA triangle similarity AAS triangle congruence analytical proof angle addition postulate ASA triangle congruence axiom biconditional conclusion 解题两个角相等 (AA) 的三角形的相似性三个角相等 (AAA) 的三角形的相似性角角边 (AAS) 三角形的全等性相等式加法性质规则系统算法应用运用把... 施 ( 用 ) 于角边角 (ASA) 三角形的全等性推测约束限制作图构造发现动态几何软件探索概括化普遍化归纳推理证明参数理由真值有效的论证推论与证明两个角相等 (AA) 的三角形的相似性三个角相等 (AAA) 的三角形的相似性角角边 (AAS) 三角形的全等性解析证明角相加的公理角边角 (ASA) 三角形的全等性公理双向条件结论 T-7686 () 1

4 conditional statement conjecture conjunction contradiction contrapositive of a statement converse of a statement counterexample deductive proof deductive reasoning definition disjunction dynamic geometry software equivalence relation Euclidean Parallel Postulate explain geometry hypotenuse and leg triangle congruence hypothesis indirect proof inductive reasoning inverse of a statement investigate justify logical equivalent negation paragraph proof parallel postulate(s) proof proof by contradiction proportional Pythagorean Theorem reason reflexive property of equality 条件陈述推测连接矛盾逆否语句经过质位变换产生的语句逆语句反例反证演绎证明演绎推理定义分离分裂动态几何软件等值关系欧几里得平行公理解释几何斜边与三角形的直角边的全等性假设间接证明归纳推理逆语句调查证明逻辑等值相反否定段落证明法平行公理证明反证法成比例的勾股定理勾股定理理由等式自反性 T-7686 () 2

5 SAS triangle congruence SAS Similarity Theorem SSS triangle congruence substitution property subtraction property of equality symmetric property of equality theorem transformational proof transitive property of equality truth value two-column proof undefined terms union of sets valid argument Communication axiom biconditional compound statement conclusion conditional statement conjecture conjunction contrapositive of a statement converse of a statement definition disjunction explain hypothesis inverse of a statement justify negation theorem 边角边 (SAS) 三角形的全等性边角边 (SAS) 三角形的相似性定理边边边 (SSS) 三角形的全等性代入性质等式减法性质等式对称性质定理变换证明等式可递性质真值两行式证明未定义词项并集合集有效的论证通信联络传送公理双向条件复合陈述结论条件陈述推测连接逆否语句经过质位变换产生的语句逆语句定义分离分裂解释假设逆语句证明相反否定定理 T-7686 () 3

6 truth value undefined terms Connections apply compound locus discover intersection of sets investigate spatial relationships union of sets Representation analytical geometry coordinate geometry definition Euclidean geometry function graphical representation locus of points logical equivalence non-euclidean geometry three dimensional space transformational geometry two dimensional space Geometric Relationships 真值未定义词项连接应用运用把... 施 ( 用 ) 于复合轨迹发现集的交点调查空间关系并集合集表述解析几何坐标几何定义欧几里得几何函数图形表述点的轨迹逻辑等值非欧几里得几何三维空间图形变换几何二维空间几何关系 AA triangle similarity 两个角相等 (AA) 的三角形的相似性 AAA triangle similarity 三个角相等 (AAA) 的三角形的相似性 AAS triangle congruence 角角边 (AAS) 三角形的全等性 ASA triangle congruence 角边角 (ASA) 三角形的全等性 absolute value 绝对值 acute angle 锐角 acute triangle 锐角三角形 T-7686 () 4

7 adjacent angles 邻角 algebraic representation 代数表述 alternate interior angles 内错角 altitude 高线顶垂线 analytical geometry 解析几何 angle 角 angle bisector 角的等分线 angle measure 角的度量 apothem 边心距 arc 弧 arc measure 弧的度量 area 面积 axis of symmetry 对称轴 base 底 ( 边 ) 底数基数 betweeness 中间性介于 bisector 等分线 center of a circle 圆心 center of a regular polygon 正多边形的中心点 center of gravity 重心 central angle 圆心角 central angle of a regular polygon 正多边形的圆心角 centroid 形心重心矩心 chord 弦 circle 圆 circumcenter 外心外接圆心 circumcircle (about a polygon) 外接圆 ( 多边形 ) circumference 圆周 collinear points 共线点 common tangents 公切线 complementary angles 余角 concave polygon 凹多边形 concentric circles 同心圆 concurrent lines 共点线 T-7686 () 5

8 cone congruence conic sections constant of proportionality convex polygon coordinate geometry coplanar corresponding angles corresponding parts corresponding sides crossection cube cylinder definition diagonals diameter dihedral angle distance distance between a point and a line distance between two parallel lines distance between two points dodecahedron ellipse endpoint equiangular equidistant equilateral triangle equilateral polygon Euclidean Geometry Euclidean Parallel Postulate exterior exterior angle external secant segment 圆锥体全等圆锥截面比例常数凸多边形坐标几何共面的对应角对应部分对应边交叉部分立方体圆柱体定义对角线直径二面角距离点与线之间的距离两条并行线之间的距离两个点之间的距离 12 面体椭圆形端点等角的等距的等边三角形等边多边形欧几里得几何欧几里得平行公理外部的外角外部割线 T-7686 () 6

9 face of a polyhedron foot of an altitude function geometric mean geometry golden ratio golden rectangle great circle hemisphere Heron's formula hexagon hypotenuse icosahedron incenter of a polygon inclination inscribed angle inscribed circle intercepted arc intercepts interior intersecting lines isosceles trapezoid isosceles triangle kite lateral area of a prism lateral edge lateral face lateral surface legs of a right triangle legs of an isosceles trapezoid length line line segment 多面体的面高线的底部函数几何平均值几何黄金比例黄金长方形大圆半圆海伦公式六边形 ( 直角三角形中的 ) 斜边二十面体多边形内心倾角斜角圆周角内切圆截弧截距内部的相交直线等腰梯形等腰三角形风筝棱柱体的侧面积侧棱侧面侧表面直角三角形的直角边等腰梯形的边长线线段 T-7686 () 7

10 linear pair locus of points major arc mean proportional measure of an angle measure of an arc median of a trapezoid median of a triangle midpoint midsegment minor arc n-gon non-collinear non-coplanar non-euclidean geometry obtuse angle obtuse triangle octagon octahedron opposite rays orthocenter orthogonal parabola parallel line segments parallel lines parallelepiped parallelogram pentagon perimeter perpendicular bisector perpendicular bisector concurrence perpendicular lines perpendicular planes 一对互为补角的角点的轨迹优弧大于半圆的弧比例中项角的度数弧的度量梯形的中线三角形的中线中点中间段小弧劣弧 n 边形不共线的不共面的非欧几里得几何钝角钝角三角形八边形八面体反向射线垂心正交的抛物线并行线段并行线平行六面体平行四边形五边形周长垂直平分线垂直平分线交点垂直线垂直面 T-7686 () 8

11 pi plane point point of concurrency point of tangency polygon polyhedron prism product property of proportions proportional pyramid Pythagorean Theorem quadrant quadratic equation quadratic formula quadrilateral radius ratio ray real numbers rectangle rectangular solid regular polygon remote interior angles rhombus right angle right triangle scalene triangle secant segment segment of a circle semicircle set 圆周率面点交点切点多边形多面体棱柱体比例的乘积性质比例的棱锥棱锥体勾股定理勾股定理象限二次方程二次公式四边形半径比率射线实数长方形长方形立体正多边形不相邻内角菱形直角直角三角形不等边三角形割线线段弓形半圆集 T-7686 () 9

12 similar polygons similar triangles simple quadrilateral skew lines slant height slope sphere square supplementary angles surface area tangent segment tangent to a circle tessellation tetrahedron three-dimensional space topology transformational geometry transversal trapezoid triangle triangle inequality trigonometry of the right triangle two-dimensional space vector vertex vertical angles vertical line volume x-axis x-intercept y-axis y-intercept z-axis 相似多边形相似三角形简单四边形斜直线斜高斜率坡度球体球面平方互补角表面积切线段圆的切线花纹镶嵌四面体三维空间拓扑学图形变换几何横截的横向的梯形三角形三角不等式直角三角形三角学二维空间矢量项点对顶角垂直线体积容积 x- 轴 x- 截距 y- 轴 y- 截距 z- 轴 T-7686 () 10

13 Constructions 作图构造 angle bisector 角的等分线 bisector 等分线 center of a regular polygon 正多边形的中心点 center of gravity 重心 circumcircle (about a polygon) 外接圆 ( 多边形 ) compass 圆规 construct 作图构造 dynamic geometry software 动态几何软件 perpendicular bisector 垂直平分线 perpendicular bisector concurrence 垂直平分线交点 perpendicular lines 垂直线 straightedge 边直尺 Locus 轨迹 circle compound locus ellipse hyperbola locus of points parabola 圆复合轨迹椭圆双曲线点的轨迹抛物线 Formal and Informal Proofs AA triangle similarity AAA triangle similarity AAS triangle congruence ASA triangle congruence angle addition postulate axiom biconditional conclusion conditional statement conjecture 正规与非正规证明两个角相等 (AA) 的三角形的相似性三个角相等 (AAA) 的三角形的相似性角角边 (AAS) 三角形的全等性角边角 (ASA) 三角形的全等性角相加的公理公理双向条件结论条件陈述推测 T-7686 () 11

14 conjunction contradiction contrapositive of a statement converse of a statement counterexample deductive reasoning definition disjunction dynamic geometry software equivalence relation Euclidean Parallel Postulate hypotenuse and leg triangle congruence indirect proof inductive reasoning inverse of a statement justify logical equivalent negation parallel postulate(s) postulate proof proof by contradiction Pythagorean Theorem reason reflexive property of equality SAS triangle congruence SAS Similarity Theorem SSS triangle congruence substitution property subtraction property of equality symmetric property of equality theorem transitive property of equality transformational proof 连接矛盾逆否语句经过质位变换产生的语句逆语句反例反证演绎推理定义分离分裂动态几何软件等值关系欧几里得平行公理斜边与三角形的直角边的全等性间接证明归纳推理逆语句证明逻辑等值相反否定平行公理公理证明反证法勾股定理勾股定理理由等式自反性边角边三角形 (SAS) 的全等性边角边三角形 (SAS) 的相似性定理边边边三角形 (SSS) 的全等性代入性质等式减法性质等式对称性质定理等式可递性质变换证明 T-7686 () 12

15 truth value two-column proof undefined terms union of sets valid argument Transformational Geometry 真值两行式证明未定义词项并集合集有效的论证变换几何 axis of symmetry 对称轴 center of a dilation 膨胀中心 center of a rotation 旋转中心 clockwise (orientation) 顺时针 ( 方向 ) composition 复合合成 constant of proportionality 比例常数 contraction 缩小 counterclockwise (orientation) 逆时针 ( 方向 ) dilation 膨胀 direct transformation 直接变换 domain 域定义域 dynamic geometry software 动态几何软件 fixed point 不懂点固定点 function 函数 function notation for transformations 函数变换符号 glide reflection 滑动反射 group 群 half-turn 转 180 度 identity 恒等式 image 映像 inverse of a transformation 逆变换 isometry 等距 mapping (function) 映像 ( 函数 ) opposite transformation 逆变换 orientation 定方向 preimage 逆象原象 reflection 反射 T-7686 () 13

16 rotation rotational symmetry symmetry tessellation transformation transformational geometry translation 旋转旋转对称对称花纹镶嵌变换变换几何转化 Coordinate Geometry abscissa analytical geometry analytical proof Cartesian coordinates Cartesian plane center-radius equation of circle coordinate coordinate geometry coordinate plane distance between two points origin point slope equation of a line rectangular coordinates slope - intercept equation of a line three-dimensional space two-dimensional space vector x-axis x-intercept y-axis y - intercept z-axis 坐标几何横坐标解析几何解析证明直角坐标笛卡尔坐标笛卡尔平面圆的中心 - 半径公式坐标坐标几何坐标平面两个点之间的距离原点线的点斜式方程式长方形坐标线的斜截式方程式三维空间二维空间矢量 x- 轴 x- 截距 y- 轴 y- 截距 z- 轴 T-7686 () 14

17 NYS Grades 9 12 Math Terms Addenda Common Core Math Standard ENGLISH F-IF.C.8 absolute-value function 绝对值函数 CHINESE S-REI.A.2 algebraic manipulation 代数运算 S-ID.B.5 categorical data 分类数据 N.C.N.4 complex plane 复平面 S-ID.B.5 conditional relative frequency 有条件的相对频率 N.C.N.5 conjugation of complex numbers 共轭复数 F-LE.A.1 constant percent rate 恒等百分率 S-ID.C.9 correlation and causation 相关性和因果关系 S-ID.C.8 correlation coefficient 相关系数 N-Q.A.3 data point 数据点 N-Q.A.2 descriptive modeling 描述性模型 A-SSE.A.1 difference of squares, example: (a 2 b 2 ) 平方的差 A-SSE.B.3 equivalent monthly interest rate 相等的月利率 F-Bf.B.3 even function 偶函数 A-CED.A.1 exponential equation 指数方程式 S-ID.B.6 fit of a function 函数的适应度 A-REI.D.12 half-plane 半平面 N-V.M.6 incidence relationship (payoff) 关联关系 S-ID.B.5 joint frequency 联合频率 S-ID.C.8 linear fit 最优线性拟合 S-ID.C8 linear phenomenon 线性现象 S-ID.C8 linearity 线性, 直线性 A-REI.D.11 logarithm function 对数函数 S-ID.B.5 marginal frequency 边际频数 A-CED.A.3 non-viable options (inequalities) 不可行选择 ( 不等式 ) N-RN.B.3 non-zero rational number 非零的有理数 F-BF.B.3 odd function 奇函数 F-IF.C.8 piece-wise defined function 分段性函数 F-BF.A.1 recursive process 递归过程 S-ID.B.6 residuals ( 统计 ) 残差 A-SSE.A.1 square of a difference, example: (a b) 2 差的平方 F-IF.C.8 step function 步阶 ( 阶跃 ) 函数 A-REI.A.1 viable argument 可行的论点 A-CED.A.3 viable options (inequalities) 可行的选择 ( 不等式 ) KEYS N-Q = Number & Quantity REI = Reasoning with Equations & Inequality SSE = Seeing Structures in Expressions VM = Vectors & Metrix quantities RN = Real Number System IF = Interpreting Functions BF = Building Functions ID = Interpreting categorical and quantitative Data ID = Interpreting categorical and quantitative Data APR = Arithmetic with Polynomials & Relational expressions CED = Creating Equations Describing numbers or relationships

7686 HS math_Geometry_Chinese_Simplified_QC2.xls

7686 HS math_Geometry_Chinese_Simplified_QC2.xls Problem Solving AA triangle similarity AAA triangle similarity AAS triangle congruence additive property of equality algorithm apply ASA triangle congruence conjecture constraints construct discover dynamic